Method and system of acoustic wave measurement of axial velocity distribution and flow rate

ABSTRACT

A method is provided to measure a distribution of axial velocities and a flowrate in a pipe or a vessel. The method comprises selecting a single cross-section at a stable-flow segment in a pipe or a vessel, installing a plurality of acoustic wave sensors along a peripheral wall of the pipe or the vessel to form a plurality of effective sound wave paths; measuring sound wave travelling time on each sound wave path; substituting the measured sound wave travelling time data into the model formulas based on a sound path refraction principle for reconstruction calculation to obtain a distribution of axial velocity in the measured cross-section of the pipe or the vessel, u(x,y); and integrating the distribution of the axial velocity u(x,y) along the cross-section to obtain a flow rate. A system is also provided to measure an axial velocity distribution and a flow rate in a pipe.

TECHNICAL FIELD

The present invention relates to the measurement on fluid flow, specifically, relates to a method and system of acoustic measurement of an axial velocity distribution and a flow rate in a pipe.

BACKGROUND

The axial velocity distribution and the flow rate in pipes and vessels are important technical parameters in the industrial or research applications. Generally, the axial velocity distribution along a cross-section is nonuniform. An effective measurement method is needed. The acoustic wave method is a suitable and advanced measurement method.

A conventional acoustic wave measurement of the axial velocity distribution in a pipe is based on the principle that the traveling time of a sound wave is influenced by the direct superposition of sound speed with a component of fluid flow velocity in the direction parallel to the sound traveling. The method has to install a certain number of acoustic wave sensors on two separate cross-sections along the axis of the pipe. The information obtained by this method is an average axial velocity distribution between the two cross-sections. The conventional method has the following drawbacks: the needs for certain number acoustic wave sensors, complicated system, stringent requirement on the pipe measuring conditions in the pipe, and influence to the measurement accuracy and precision to some extents by the sound path curvature caused by the axial velocity.

In order to solve the existing problems as described above, people are always seeking an ideal technique solution.

SUMMARY OF THE INVENTION

The objective of this invention is to overcome the drawbacks of the present technologies, and provide a method and system of acoustic wave measurement of the axial velocity distribution in a pipe.

In order to achieve the above objectives, the technical solution of this invention is to provide an acoustic method to measure an axial velocity distribution and the flow rate in a pipe. The method comprises:

selecting a single cross-section at a stable segment or an interested segment in the pipe or a vessel, and installing a plurality of acoustic wave sensors along a peripheral wall of the cross-section, wherein a plurality of effective sound wave paths are formed between the plurality of acoustic wave sensors, wherein a sound wave path between one pair of acoustic wave sensors corresponds to only one effective sound wave path;

measuring a sound wave travelling time on each sound wave path, respectively;

substituting the sound wave travelling times on all sound wave paths into the follow formula, so that the axial velocity distribution u(x,y) can be obtained via reconstruction;

${{{\int_{l_{i}}{{u\left( {x,y} \right)}\sqrt{1 + \left( y^{\prime} \right)^{2}}d\; x}} = {L_{i}\mspace{14mu} \sqrt{c^{2} - \left( \frac{L_{i}}{\Delta \; t_{i}} \right)^{2}}}},{i = 1},2,\ldots \mspace{14mu},N}\ $

where, l_(i) is the ith sound wave path, L_(i) is a distance between the two acoustic sensors at the ith path, Δt_(i) is the sound wave traveling time along the ith effective sound wave path, N is the number of effective sound wave paths, c is the sound speed at the measuring physical conditions of the medium;

integrating the axial velocity u(x,y) obtained from above step along the cross-section to obtain the flow rate in the pipe.

Based on the above, the method includes measuring two traveling times of sound waves between two acoustic wave sensors in opposite directions, respectively, and the average of these two traveling times is the travelling time of sound wave on this effective sound wave path.

Based on the above, each acoustic wave sensor emits sound waves in turn, when one acoustic wave sensor emits sound wave, the rest of the acoustic wave sensors record the sound wave and the frequency of all acoustic wave sensors is the same.

Based on the above, each two to three acoustic wave sensors emit sound waves simultaneously, wherein each acoustic wave sensor has different transmitting frequencies, and identifiable by wave filtering.

Based on the above, the acoustic wave sensor has the function of both emitting and receiving sound waves.

Based on the above, the acoustic wave sensor is a combination of a sound wave transmitter and a sound wave receiver.

Based on the above, the axial velocity distribution u(x,y) is calculated by fitted with Taylor series expansion.

Based on the above, when the axial velocity distribution u(x,y) accords with characteristics of a jet flow, the axial velocity distribution u(x,y) can also be calculated with approximate fitting using Gaussian function:

${{u\left( {x,y} \right)} = {{U\; e^{- \frac{{({x - x_{0}})}^{2} + {({y - y_{0}})}^{2}}{2\; \sigma^{2}}}} + u_{0}}},$

where (x₀,y₀) is the coordinates of the point of maximum velocity, U is the maximum velocity of the jet, u₀ is the base velocity at the far edge of the jet, and σ is the expansion width.

Based on the above, the selected cross-section intersects the axis of the pipe or vessel in a right-angle or an approximate right-angle.

According to another aspect, this invention provides a system on acoustic measurement of an axial velocity distribution and a flow rate in a pipe. The system includes a plurality of acoustic wave sensors installed on a peripheral wall of a cross-section in the pipe or the vessel; a digit to analog converter card, an analog to digit converter card, and a measuring computer for measurement. The measurement software to implement the above described acoustic measuring method was installed in the measuring computer to measure the axial velocity distribution and the flow rate;

The digit to analog conversion card is connected with the computer for measurement and the acoustic wave sensors, respectively, to transfer the frequency digital signals coded with the measurement software into analogue acoustic signals and the sound wave is emitted by the acoustic wave sensors.

The analog to digit conversion card is connected with the measuring computer and the acoustic wave sensors, respectively, to transfer the collected acoustic signals in the pipe into digital signals and input into the measuring computer.

The measuring computer, via the measurement software, controls the acoustic sound wave sensors to emit sound waves, measure the sound traveling time on an effective sound wave path from each acoustic wave sensor to other acoustic wave sensors, and substitute the sound traveling times on each effective sound wave path into the following reconstruction formula for axial velocity distribution on cross sections in a pipe or a vessel to obtain u(x, y).

${{{\int_{l_{i}}{{u\left( {x,y} \right)}\sqrt{1 + \left( y^{\prime} \right)^{2}}d\; x}} = {L_{i}\mspace{14mu} \sqrt{c^{2} - \left( \frac{L_{i}}{\Delta \; t_{i}} \right)^{2}}}},{i = 1},2,\ldots \mspace{14mu},N}\ $

wherein, is the ith sound path, L_(i) is a distance between the two acoustic wave sensors at the ith path, Δt_(i) is the traveling times of the sound waves along the ith sound wave path, N is the number of effective sound wave paths, c is the sound speed at the measuring physical conditions of the medium;

The measuring computer; via the measuring software, integrates the obtained axial velocity distribution u(x,y) along the cross-section; so that the flow rate in the pipe is obtained.

Compared to the conventional techniques, this invention possesses predominant virtues and remarkable advances. Specifically, this invention measures the axial velocity distribution and the flowrate using the data of the sound wave traveling times between the acoustic wave sensor at a single measurement cross-section and reconstructing axial velocity distribution in the pipe or vessel based on a sound wave path curvature theory. Compared to the conventional acoustic measurement methods; this invention needs half of the number of acoustic wave sensors for similar measurement precision, have advantages of smaller errors; higher precision; and higher reliability. Further, the accuracy of this invention is not affected by the following factors: whether the measured cross-section is exactly perpendicular to the axis of the pipe, whether the acoustic wave sensors are evenly installed on the peripheral of the measured cross-section, whether the reconstruction formulas on the axial velocity distribution are varied appropriately, etc.

The method disclosed by this invention can apply to effectively measure an axial velocity distribution and a flow rate in a pipe containing gas, liquid, and two-phase or multi-phase flow in a pipe. It can apply to measurement of an axial flow field in a combustion chamber, a jet flow, a fluidized bed, a chemical reactor, and a jet flow in open space.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of an axial velocity distribution along one dimension x direction, and corresponding sound wave path.

FIG. 2 is a schematic configuration of the measurement method of this invention.

FIG. 3 is an axial velocity distribution of a preset simulation flow field in a round cross-section pipe, in which the flow field center resides at the geometric center of the pipe.

FIG. 4 shows the reconstruction relative errors of an axial velocity distribution in a flow field having a center at a geometric round center, using six groups of acoustic wave sensors to simulate measurement in a round cross section pipe with 3 order fitting precision by Taylor series expansion.

FIG. 5 shows the reconstruction relative errors of an axial velocity distribution in a flow field having a center at the geometric round center, using 6 groups of acoustic wave sensors to simulate measurement in a round cross section pipe with 4 order fitting precision by Taylor series expansion.

FIG. 6 is an axial velocity distribution of a preset simulation flow field in a round cross-section pipe, which flow center deviated from the geometric center of the pipe.

FIG. 7 shows the reconstruction relative errors of an axial velocity distribution in a flow field having a center deviated from a geometric round center, using 6 groups of acoustic wave sensors to simulate measurement in a round-cross section pipe with 3 order fitting precision by Taylor series expansion.

FIG. 8 shows the reconstruction relative errors of the axial velocity distribution in a flow field having a center deviated from a geometric round center, using 6 groups of acoustic wave sensors to simulate measurement in a round cross section pipe with 4 order fitting precision by Taylor series expansion.

FIG. 9 shows the reconstruction relative errors of the axial velocity distribution in a flow field having a center at a geometric round center, using 8 groups of acoustic wave sensors to simulate measurement in a round cross section pipe with 3 order fitting precision by Taylor series expansion.

FIG. 10 shows the reconstruction relative errors of the axial velocity distribution in a flow field having a center deviated from a geometric round center, using 8 groups of acoustic wave sensors to simulate measurement in a round cross section pipe with 4 order fitting precision by Taylor series expansion.

Hereinafter, the present invention will be described in detail with reference to the drawings.

As shown in FIG. 2, an acoustic method measuring the axial velocity distribution and the flow rate comprises the following steps:

selecting a single cross-section at a flow-stable segment or an segment of interest in a pipe or a vessel, and installing a plurality of acoustic wave sensors on a peripheral wall of the pipe or the vessel at the cross-section; the number of the acoustic wave sensors may be determined according to the complicity of the flow field, and preferably four to eight acoustic wave sensors are installed, wherein the acoustic wave sensor may be a unitary sensor integrating with both functions of acoustic signal emission and reception; or the acoustic wave sensor may be a combination of an acoustic signal emitter and an acoustic signal receiver;

measuring a sound wave traveling time on all sound wave paths, wherein a plurality of effective sound wave paths are formed between the plurality of acoustic wave sensors, the sound paths between a pair of acoustic wave sensor is counted as one effective sound wave path, specifically, measuring two sound wave traveling times on each sound wave path in opposite directions of the two acoustic wave sensors, an average sound wave traveling time of the two sound wave traveling times is used as a sound traveling time of an effective sound wave path;

substituting the sound wave traveling time on each sound wave path into the follow formula to reconstruct an axial velocity distribution u(x,y) so as to obtain the axial velocity distribution;

${{{\int_{l_{i}}{{u\left( {x,y} \right)}\sqrt{1 + \left( y^{\prime} \right)^{2}}d\; x}} = {L_{i}\mspace{14mu} \sqrt{c^{2} - \left( \frac{L_{i}}{\Delta \; t_{i}} \right)^{2}}}},{i = 1},2,\ldots \mspace{14mu},N}\ $

where, l_(i) is an ith sound wave path, L_(i) is a distance between the two acoustic wave sensors at the ith effective sound wave path, Δt_(i) is the sound wave traveling time along the ith sound wave path, N is the number of effective sound wave paths, c is the sound traveling speed in a medium in the pipe or the vessel at the measuring physical conditions; and

The flow rate in the pipe can be obtained by integrating the axial velocity u(x,y) along the cross-section. Preferably, every acoustic wave sensor emits sound wave in turn, and the frequency of the acoustic signal from each acoustic wave sensor is the same. When one acoustic wave sensor emits a sound wave, the rest of other acoustic wave sensors record this sound wave. Typically, the acoustic measurement takes approximately 2 seconds to complete. Since the flow field is relatively steady, the effect of such sound emitting method on the measurement precision is very small.

Preferably, every two to three acoustic wave sensors emit sound waves simultaneously, and each acoustic wave sensor emits sound wave at different frequencies. Compared with the method that every acoustic wave sensor emits sound wave in turn, this approach takes shorter time to finish one complete measurement on the axial velocity distribution in the pipe or the vessel. However, using different frequencies simultaneously in one measurement may have difficulty for effective identification of acoustic signals from each other.

In practical application; whether to control the acoustic wave sensor to emit the sound wave in turn or control every 2-3 acoustic wave sensors to emit sound wave simultaneously can be determined according to the time required to complete the measurement.

It should be noted that the suitable measurement acoustic frequency can be selected based on the size of the measured object and the properties of the flow medium. For gas or multiphase medium, the attenuation rate of sound wave is proportional to the square of the frequency, hence the sound wave would attenuate quickly with increase of the sound wave frequency. However, the larger the frequency is, the more favorable the condition to achieve high precision of obtaining the sound wave travelling time, and thus high precision of measurement results of the axial velocity distribution. A high measurement sound frequency should be used as long as the sufficient intensity of acoustic signals at the ends of the sound paths can be achieved so as to ensure the measurement accuracy.

In order to diminish the influence of the radial component of the flow velocity within the measured cross-section in the pipe, the average of the two sound wave travelling time along each sound wave path in opposite directions is taken as the sound wave traveling time in the reconstruction. In exemplary embodiments, 4, 5, 6, 7, 8 acoustic wave sensors are evenly installed around the measured cross-section form 6, 10, 15, 21, 28 sound wave effective paths, respectively, as illustrated in FIG. 2.

Specifically, the axial velocity distribution u(x,y) is fitted with Taylor series expansion for reconstruction. Taking the 3^(rd) order for example,

u(x,y)=C ₁ +C ₂ x+C ₃ y+C ₄ x ² +C ₅ xy+C ₆ y ² +C ₇ x ³ +C ₈ x ² y+C ₉ xy ² +C ₁₀ y ³ +o(x,y)

where o(x,y) is the infinitely small quantity term, C₁, C₂, . . . , C₁₀ are the polynomial coefficients to be determined. The precision of the fitting polynomial, and correspondingly the number of the terms, is determined by the complexity of the axial flow field. Correspondingly, the number of effective sound wave paths formed by the acoustic wave sensors should be no less than the number of the fitting polynomial coefficients.

If the axial velocity distribution u(x,y) accords with characteristics of a free jet flow, a Gaussian polynomial can be sued for reconstruction:

${{u\left( {x,y} \right)} = {{U\; e^{- \frac{{({x - x_{0}})}^{2} + {({y - y_{0}})}^{2}}{2\; \sigma^{2}}}} + u_{0}}},$

where (x₀,y₀) is the coordinates of the point of maximum velocity, U is the maximum velocity magnitude of the jet flow with the Gaussian distribution, u₀ is the base velocity at the far edge of the jet away from the center of the jet flow, and σ is the expansion width. The number of effective sound wave paths determined by the corresponding number of acoustic wave sensors should be no less than 5.

Specifically, the measured cross-section in a pipe or a vessel intersects an axis of a pipe or a vessel. The cross-section may be perpendicular or substantially perpendicular to the axis of the pipe or the vessel. The acoustic wave sensors may be installed around a peripheral wall of the cross-section evenly, also, the acoustic wave sensors may be installed unevenly around peripheral wall of the measured cross-section according to the characteristics of the axial flow profile such that more sound wave paths are obtained for the flow field with relatively complex variations of axial velocity.

Additionally, the shape of the cross-section of the measured object, as well as certain variations of the reconstruction formulas for the axial velocity distribution, would not influence the effect of this invention.

The measurement methods of this invention are suitable for the pipes and vessels with different cross-section shapes such as circular, elliptical, and rectangular etc. Therefore, reconstructing the axial velocity distribution for a circular cross-sectional pipe is used as an example to validate the acoustic measurement method of this invention.

As shown in FIG. 2, a cross-section within a stable-flow segment in a circular cross-sectional pipe is selected, and six acoustic wave sensors are disposed around a peripheral wall of the measured cross-section of the pipe, Other conditions include: the diameter of the pipe is 1 meter, the medium is air, and the temperature is room temperature. The preset axial velocity distribution is reconstructed by the method of this invention using a simulated acoustic measurement.

Taking the geometric center of the cross-section of the pipe as the coordinate origin, the preset simulation axial velocity field of the round cross section in the pipe with a center of the flow field at the geometric center is constructed as u₀(x, y)=5e^(−(x) ² ^(+y) ² ⁾, as shown in FIG. 3.

Via integrating along sound wave paths shown in FIG. 2, all sound wave travelling times are obtained and shown as in Table 1, wherein 6 digits after decimal point are kept.

TABLE 1 Sound wave travelling time along each path within the simulated pipe, as shown in FIG. 3, in pipe (unit: ms) Path AB CB DC ED EF FA EA AC Time 1.456953 1.456978 1.456953 1.456953 1.456978 1.456953 2.523436 2.523436 Path EC FB DB FD DA EB FC Time 2.523593 2.523593 2.523436 2.523436 2.914016 2.913950 2.913950

Based on the above acoustic method to measure the axial velocity distribution and flow rate, and by using a 3 order precision fitting to calculate the axial velocity distribution u(x,y), the results of reconstructed flow field u(x,y) with the acoustic simulation measurement is obtained. The relative reconstruction errors are shown in FIG. 4. Moreover, the reconstructed axial velocity distribution u(x,y) with a 4 order precision Taylor series expansion is conducted and the relative reconstruction error is shown in FIG. 5.

As can be seen, the simulated acoustic measurement is sufficiently accurate and reliable. And when the fitting precision with Taylor series expansion is increased, the simulated measurement precision is also increased correspondingly.

Similarly, a preset simulation field may be built with the flow center deviating from the geometric center in a round cross section of a pipe, and a center of the round cross section is used as an origin of a coordinate. The preset axial velocity distribution in the pipe is determined using the equation u₀(x,y)=5e^(−(1.5(x−0.1)) ² ^(+(y+0.15)) ² ⁾, as shown in FIG. 6.

By integrating along sound wave paths shown in FIG. 2, all sound wave travelling times are obtained and shown as in Table 2, wherein 6 digits are remained behind a decimal point.

TABLE 2 Sound wave traveling along each path within the simulated pipe of FIG. 6, in pipe (unit: ms) Path AB CB DC ED EF FA EA AC Time 1.456937 1.456978 1.456972 1.456950 1.456937 1.456923 2.523421 2.523432 Path EC FB DB FD DA EB FC Time 2.523598 2.523542 2.523440 2.523428 2.913999 2.913926 2.913928

Based on the above acoustic method to measure the axial velocity distribution and flow rate, and using a precision fitting of 3 order and 4 order of Taylor series, respectively, to calculate the axial velocity distribution u(x,y), the reconstructed flow field result u(x,y) is obtained with the acoustic simulation measurement. The reconstruction errors are given in FIGS. 7 and 8, respectively. Similarly, it can be seen that the simulated acoustic measurement is sufficiently accurate and reliable. And when the fitting precision with Taylor series expansion is increased, the simulated measurement precision by the acoustic measurement is increased correspondingly. That is, the precision of acoustic measurement is affected by the fitting precision of Taylor series expansion.

To further determine the influence factors to the precision of the acoustic wave measurement, the simulated acoustic measurements in a round cross section of a pipe was conducted with eight set acoustic wave sensors, using Taylor series expansion fitting precision of 3 order and Taylor series expansion fitting precision of 4 order, respectively. The relative reconstruction errors of the axial velocity distribution for the acoustic measurement are illustrated in FIGS. 9 and 10, respectively.

As it can be seen, in addition to the conclusion that the precision of the acoustic measurement is influenced by the fitting precision with Taylor series expansion, eight sets of acoustic wave sensors do not show significant improvement to the simulated measurement results compared with using 6 sets of acoustic wave sensors.

The above two typical exemplary scenarios of simulated acoustic measurements of the axial velocity distribution show that the acoustic measurement of axial velocity distribution in a pipe is feasible and also reliable, and the acoustic measurement is based on the mechanism of sound wave path bending caused by a flow to the sound propagation direction. Further, the precision of the acoustic measurement is affected by the precision of order of fitting series and irrelevant to the number of acoustic wave sensors used. However, as the fitting precision of series is increased, the number of acoustic wave sensors needs to be increased correspondingly to solve the equation because of the increase of number of coefficients needed.

According to another aspect, this invention provides a system on acoustic measurement of the axial velocity distribution and the flow rate in a pipe. The system comprises a plurality of acoustic wave sensors installed on the peripheral wall of a measured cross-section in a pipe or a vessel, a digit to analog converter card, an analog to digit converter card, and a measuring computer. The measuring computer includes a preset measurement software to measure the axial velocity distribution and the flow rate as described above.

The digit to analog converter card is connected with the measuring computer and the acoustic wave sensors, respectively, to transfer the digital signals coded with the measurement software into analogue acoustic signals, and emit the acoustic signals by the acoustic wave sensors.

The analog to digit converter card is connected with the measuring computer and the acoustic wave sensors, respectively, to transfer the collected acoustic signals into digital signals and input into the measuring computer.

The measuring computer controls, via the measurement software, the acoustic wave sensors to emit sound waves, measure the sound wave travelling time on the sound wave paths from each acoustic wave sensor to all other acoustic wave sensors, and substitute the sound wave travelling times into the reconstruction formula for an axial velocity distribution in a pipe or a vessel to obtain the axial flow distribution u(x,y):

${{{\int_{l_{i}}{{u\left( {x,y} \right)}\sqrt{1 + \left( y^{\prime} \right)^{2}}d\; x}} = {L_{i}\mspace{14mu} \sqrt{c^{2} - \left( \frac{L_{i}}{\Delta \; t_{i}} \right)^{2}}}},{i = 1},2,\ldots \mspace{14mu},N}\ $

wherein, l_(i) is the ith sound wave path, L_(i) is a distance between the two acoustic sensors at the two ends of the ith path, Δt_(i) is the average of the two sound wave travelling times of the sound waves along the ith sound path in opposite directions, N is the number of effective wave sound paths, c is the sound speed at the measuring medium in the pipe or the vessel at the measuring conditions;

The measuring computer, via the preset measuring software, integrates the obtained axial velocity distribution u(x,y) along the cross-section, so that the flow rate is obtained.

The method of the present invention is suitable to different media in a pipe, such as gas, liquid, two-phase or multiphase media for effective measurements to the axial velocity distribution and the flow rate in the pipe. Furthermore, the method of the present invention can be used to measure flow fields in a combustion chamber, a fluidized bed, a chemical reactor, and an open jet flow, etc.

It should be noted that the exemplary embodiments are just used to describe the technical solution of t the present invention, and are not restricted to the exemplary embodiments. Although the invention is described in detail with reference to the preferred exemplary embodiments. The technicians in the related arts should understand that: the exemplary embodiments of the present invention can be modified or the technical characteristic can be substituted without depart from the spirit of the present invention, and all should be covered in the scope of the technical solutions of the present invention. 

1. A method of acoustic wave measurement of an axial velocity distribution in a pipe or a vessel, comprising: selecting a single cross-section located at a stable-flow segment in the pipe or the vessel; installing a plurality of acoustic wave sensors along a peripheral wall of the pipe or the vessel at the cross-section, wherein a plurality of effective sound wave paths are formed between the acoustic wave sensors; measuring a sound wave travelling time along each sound wave path by the plurality of acoustic wave sensors; and substituting the sound wave traveling time of each sound wave path into a reconstruction equation to obtain the axial velocity distribution u(x,y) on the cross section of the pipe or the vessel to obtain the axial velocity distribution, wherein the axial velocity distribution u(x,y) is an axial velocity at a point (x, y) in a coordinate system, the reconstruction equation is a function that correlates the axial velocity distribution u(x, y) with each distance between two acoustic wave sensors at two ends of a sound wave path, and a sound traveling time along the sound wave path.
 2. The method of claim 1, wherein a formula below is used as the reconstruction equation: ${{{\int_{l_{i}}{{u\left( {x,y} \right)}\sqrt{1 + \left( y^{\prime} \right)^{2}}d\; x}} = {L_{i}\mspace{14mu} \sqrt{c^{2} - \left( \frac{L_{i}}{\Delta \; t_{i}} \right)^{2}}}},{i = 1},2,\ldots \mspace{14mu},N}\ $ wherein, l_(i) denotes an ith sound wave path, L_(i) is a distance between the two acoustic wave sensors at two ends of an ith sound wave path, Δt_(i) is the sound traveling time along the ith sound wave path, N is a number of effective sound wave paths, c is a static sound speed at measuring physical conditions of a medium in the pipe or the vessel and wherein measuring a sound wave travelling time along each sound wave path includes measuring sound wave travelling times along each sound wave path in opposite directions, respectively, and an average of the sound travelling times along the each sound wave path in opposite directions is a sound wave travelling time in an effective sound wave path.
 3. The method of claim 2, wherein each acoustic wave sensor emits sound waves in turn, and when one acoustic wave sensor emits a sound wave, the rest of the acoustic wave sensors record the sound wave to measure the sound wave traveling time and wherein all of the acoustic wave sensors emit sound waves with the same frequency.
 4. The method of claim 2, wherein every two to three acoustic wave sensors emit sound waves simultaneously with different frequencies for each, and wherein the sound waves are identifiable by filtering.
 5. The method of one of claim 2, wherein the acoustic wave sensor has an integrated function of both emitting a sound wave and receiving acoustic signals, or the acoustic wave sensor is a combination of a sound wave emitter and a sound wave receiver.
 6. (canceled)
 7. The method of claim 2, wherein the axial velocity distribution u(x,y) is reconstructed by fitting with a polynomial of Taylor series expansion.
 8. The method of claim 2, wherein, when the axial velocity distribution is characterized as a free jet flow, the axial velocity distribution u(x,y) along the cross-section is reconstructed with proximate fitting with a Gaussian formula below: ${u\left( {x,y} \right)} = {{U\; e^{- \frac{{({x - x_{0}})}^{2} + {({y - y_{0}})}^{2}}{2\; \sigma^{2}}}} + u_{0}}$ where (x₀,y₀) is coordinates of a point of a maximum velocity, U is the maximum velocity of the jet flow, u₀ is a velocity at a far edge of the jet flow, and σ is a expansion width.
 9. The method of claim 2, wherein the measured cross-section in the pipe or the vessel is perpendicular or approximately perpendicular to an axis of the pipe or an axis of the vessel.
 10. (canceled)
 11. The method of claim 2, further comprising integrating the axial velocity distribution u(x,y) along the cross-section to obtain a flow rate in the pipe or the vessel.
 12. The method of claim 2, wherein the plurality of acoustic wave sensors include four, five, six, seven or eight acoustic sensors.
 13. The method of claim 2, wherein the plurality of acoustic wave sensors are installed evenly along the peripheral wall of the pipe or the vessel.
 14. The method of claim 2, wherein the plurality of acoustic wave sensors are installed unevenly along the peripheral wall of the pipe or the vessel according to characteristics of an axial flow field.
 15. The method of claim 2, wherein the cross section forms an angle of substantially 90 degrees or an angle greater or less than 90 degrees with an axis of the pipe or the vessel.
 16. A system to measure an axial velocity distribution and a flow in a pipe or in a vessel, comprising a plurality of acoustic wave sensors disposed on a peripheral wall around a single cross-section of the pipe or the vessel; a digit to analog converter card; an analog to digit converter card; a measuring computer including: one or more processors, a memory, and a plurality of instructions stored in the memory and executable by the one or more processors; wherein the digit to analog converter card is connected to the measuring computer and the plurality of acoustic wave sensors, and configured to transfer coded by the one or more processors to analogue acoustic signals, and the analogue acoustic signals are emitted by the plurality of acoustic wave sensors; wherein the analog to digit converter card is connected to the plurality of acoustic wave sensors and the measuring computer and configured to transfer the analogue acoustic signals collected by the plurality of acoustic wave sensors into digital signals, and input the digital signals into the measuring computer; and wherein the one or more processors are configured to control the plurality of acoustic wave sensors to emit sound waves and instruct the acoustic wave sensors to measure a sound wave travelling time on each sound wave path between one acoustic wave sensor to all the other acoustic wave sensors, and determine the axial velocity distribution by substituting the measured sound wave traveling times into a reconstruction formula below to reconstruct the axial velocity distribution u(x,y) along the cross-section in the pipe or the vessel to obtain the axial velocity distribution via reconstruction, ${{{\int_{l_{i}}{{u\left( {x,y} \right)}\sqrt{1 + \left( y^{\prime} \right)^{2}}d\; x}} = {L_{i}\mspace{14mu} \sqrt{c^{2} - \left( \frac{L_{i}}{\Delta \; t_{i}} \right)^{2}}}},{i = 1},2,\ldots \mspace{14mu},N}\ $ where, l_(i) is an ith sound wave path, L_(i) is a distance between two acoustic wave sensors at two ends of an ith sound wave path, Δt_(i) is an average of two sound wave traveling times along the ith sound wave path, N is a number of effective sound wave paths, c is a static sound speed at a medium in the pipe or the vessel at measuring physical conditions.
 17. The system of claim 16, wherein the one or more processors are further configured to integrates the axial velocity u(x,y) along the cross-section to obtain the flow rate in the pipe or in the vessel.
 18. The system of claim 16, wherein the axial velocity distribution u(x,y) is reconstructed by fitting with a polynomial of Taylor series expansion for reconstruction with acoustic measurement.
 19. The system of claim 16, wherein, when the axial velocity distribution is characterized as a free jet flow, the axial velocity distribution along the cross-section is reconstructed by proximate fitting with a Gaussian formula: ${u\left( {x,y} \right)} = {{U\; e^{- \frac{{({x - x_{0}})}^{2} + {({y - y_{0}})}^{2}}{2\; \sigma^{2}}}} + u_{0}}$ where (x₀,y₀) is coordinates of a point of a maximum velocity, U is the maximum velocity of the jet flow, u₀ is a velocity at a far edge of the jet flow, and a is a expansion width.
 20. The system of claim 16, wherein the plurality of acoustic wave sensors include four, five, six, seven or eight acoustic sensors.
 21. The system of claim 16, where only one sound wave path is counted as an effective sound wave path between one pair of the acoustic wave sensors, and wherein measuring a sound wave travelling time along each sound wave path including measuring sound wave travelling times along each sound wave path in opposite directions, respectively and an average of sound travelling times along the each sound wave path in opposite directions is a sound wave travelling time in an effective sound wave path. 